Question

the legs of an isosceles triangle measure x + 5 and 2x - 6. the base of the same triangle measures 3x - 2. find the length of the base.

Explanation:

Step1: Set leg lengths equal

In an isosceles triangle, the two legs are equal. So, set \( x + 5 = 2x - 6 \).

Step2: Solve for x

Subtract \( x \) from both sides: \( 5 = x - 6 \). Then add 6 to both sides: \( x = 11 \).

Step3: Find base length

Substitute \( x = 11 \) into the base formula \( 3x - 2 \). So, \( 3(11) - 2 = 33 - 2 = 31 \).

Answer:

31